Question

A spinner has five congruent sections, one each of blue, green, red, orange, and yellow. Yuri spins the spinner 10 times and records his results in the table.

A 2-column table has 5 rows. The first column is labeled Color with entries blue, green, red, orange, yellow. The second column is labeled Number with entries 1, 2, 0, 4, 3.

Which statements are true about Yuri’s experiment? Select three options.

The theoretical probability of spinning any one of the five colors is 20%.
The experimental probability of spinning blue is One-fifth.
The theoretical probability of spinning green is equal to the experimental probability of spinning green.
The experimental probability of spinning yellow is less than the theoretical probability of spinning yellow.
If Yuri spins the spinner 600 more times and records results, the experimental probability of spinning orange will get closer to the theoretical probability of spinning orange.

Answer 1

True statements:
- The theoretical probability of spinning any one of the five colors is 20%.
- The theoretical probability of spinning green is equal to the experimental probability of spinning green.
- If Yuri spins the spinner 600 more times and records results, the experimental probability of spinning orange will get closer to the theoretical probability of spinning orange.

Work: theoretical probability = 1/5 = 20%. Experimental probabilities from 10 spins: blue 1/10, green 2/10 = 1/5, yellow 3/10. So blue is not 1/5 and yellow’s experimental probability (0.3) is greater than theoretical (0.2). The last statement is justified by the law of large numbers (more trials tend to make experimental frequencies approach theoretical probabilities).